Rheology of Polymeric Fluids

Chapter 1. Introduction: Polymers and Rheology Polymers
Basic molecular motions and forces in polymer fluids with long flexible chains
Equilibrium properties of a single polymeric chain
Non-equilibrium properties of a single polymeric chain in dilute polymer solutions
Qualitative physics of molecular motions in polymer melts
Concept of rheology and specifics of polymer rheology
Questions to Chapter 1
References to Chapter 1

Chapter 2. Linear Viscoelasticity
Introductory remarks.
Linearity
Two classical rheological models
The model of Hookean solids
The model of Newtonian liquids
General principles of designing viscoelastic models
Kelvin-Voight model
Maxwell model
Limit transitions in viscoelastic models. Trivial models
"Standard" model of viscoelastic solids. Duality
"Standard" model of viscoelastic liquids. Duality
Deborah and Weissenberg numbers
General viscoelastic relations. Principle of superposition
Deformation modes in linear liquid-like viscoelasticity
Concluding remarks on linear viscoelasticity
Problems to Chapter 2
Questions to Chapter 2
References to Chapter 2

Chapter 3. Elements of Continuum Mechanics Fundamental Concepts
Kinematics of continuum
Kinematical concepts; definitions
Basic kinematical tensors; Helmholtz theorem
Geometrical characteristics of deformation
Compatibility
Distributed Forces in Continuum Mechanics
Concept of distributed forces
Stress vectors and stress tensor
Internal rotations. Symmetry of stress tensor. Principal stresses
Balance Relations (Conservation Laws) in Continuum Mechanics
Mass balance
Momentum balance
Energy balance
Problems to Chapter 3
Questions to Chapter 3
References to Chapter 3

Chapter 4. Viscoelastic Constitutive Equations Linear 3D Constitutive Equations
3D constitutive equations for linear elasticity
3D linear constitutive relation for incompressible viscous liquids
3D extension of linear constitutive equations for viscoelastic incompressible liquids
Principles of Invariance and Nonlinear Generalizations of Maxwell model
Invariance of constitutive equations relative to time shift
Galilean invariance
Material objectivity. Co-rotational (Jaumann) derivative and related nonlinear extensions of Maxwell model
Convected tensor time derivatives and respective constitutive equations of Maxwell type
"Mixed" upper and lower convected time derivatives and related Maxwell type constitutive equations
More General Class of Maxwell Type Models
Two Examples
UCM model
Simple version of LM model
Viscoelastic Constitutive Equations of Integral Type
Rheological Parameters. Thermo-Rheological Simplicity. Non-Isothermal.
Problems to Chapter 4
Questions to Chapter 4
References to Chapter 4

Chapter 5. Basic Simple Flows. Predictions Some of some Viscoelastic Constitutive Equations and their Comparison with Data Simple Shear
Structure of basic tensors; momentum balance; definitions
Component form of two viscoelastic constitutive equations in simple shear and their predictions of stresses
Regimes (modes) of shearing for viscoelastic models and comparisons with data
A) Linear viscoelastic region
B) Steady flow in nonlinear shearing region
C) Transient nonlinear deformations under given constant shear rate
D) Transient nonlinear deformation under given shear stress

E) Steady nonlinear shear oscillations
Concluding remarks on simple shearing
Elongational flows
General concept
Simple (uniaxial) elongation
General relations
Model equations
Regimes (modes) of deformations
Steady elongational flow in nonlinear region of deformations
Improvement of constitutive equations
Transient nonlinear start up flows under given constant elongational rate
Recoverable strains in simple extensional flow
Creep and recovery under given constant elongational stress
Transient nonlinear flow under given elongational force
Concluding remarks on simple elongation
Equi-biaxial extension
General relations
Model equations
Deformation modes and steady flow
Concluding remarks on the equi-biaxial elongation
Problems to Chapter 5
Simple shear
Elongational flows
Questions to Chapter 5
References to Chapter 5

Chapter 6. Experimental Methods in Rheology of Viscoelastic Liquids Simple Shear Tests
Parallel plate device
Cone-plate rheometer. Basic relations.
Cone-plate: schemes of instruments; methods of measurements
Methodical remarks
Disc-disc rheometer
Capillary rheometry
Experimental Methods in Uniform extension of Liquid Polymers
Schemes of instruments
Methodological aspects
Defects in schemes of devices and errors in measurements
Experimental Methods in Non-Uniform Extension of Liquid Polymers
Weakly non-uniform extension
Schemes of devices for drawing of elastic liquids from a resevoir
Drawing out of a capillary
Methodological observations
Methods of Flow Birefringence
Problems to Chapter 6
Questions to Chapter 6
References to Chapter 6

Chapter 7. Flows of Polymers in Channels and Pipes Poiseuille Flows of Viscoelastic Liquids in Capillaries and Die Slits
Steady Flows of Viscoelastic Liquids in Long Tubes with Arbitrary Cross-Sections
Enhancement of Flow Rate by Using Pulsating Pressure
Entrance and exit Steady Flows
Extrudate Swell
Questions to Chapter 7
References to Chapter 7

Chapter 8. Unstable Flows of Polymeric Fluids Instabilities in flows of Polymers in Dies and Pipes ("Melt Fracture")
Experimental data
Mechanisms of melt flow instabilities
Draw Resonance in Melt Spinning and Flat Film Extrusion
Bubble Instability in Film Blowing
Questions to Chapter 8
References to Chapter 8

Appendix A: Cartesian Tensor Calculus and Remarks on General Tensor Analysis
A1. Orthogonal transformations and orthogonal matrices
A2. Vectors
A3. Definition of tensors
A4. General tensor algebra
A5. Algebraic properties of second-rank tensors
A6. Time-space dependent tensor fields. Differentiation of tensors with respect to time and space variables
A7. Remarks on general tensor analysis
Problems for Cartesian tensor calculus
Questions to Cartesian tensor calculus
References to Appendix A

Appendix B: Component Form of Some Equations in Continuum Mechanics
B1. Momentum Balance and Continuity Equations
B2. Component Form for the Velocity Gradient Tensor
B3. Heat Equation

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